Summary: By making only use of the Schauder fixed point theorem, we establish an existence result for a singular nonlinear two-point boundary value problem of the form \[ \begin{aligned} & y^{(n)}+g(x,y,y',\dots,y^{(n-1)})=0,\quad 0<x<1,\\ & y^{(i)}(0)=0,\quad 0\leq i\leq k-1;\quad y^{(j)}(1)=0,\quad k\leq j\leq n-1,\end{aligned} \] where \(1\leq k\leq n-1\) is fixed and \(g(x,y_1,\dots,y_n)\) is a Carathéodory function allowed to possess singularities at \(y_i=0\), \(1\leq i\leq n\).